当前位置:首页 >> >> 现代控制工程CH06 Compensation of the Control Systems_图文

现代控制工程CH06 Compensation of the Control Systems_图文

CH.6 Compensation of control systems

Stability criterion in the Bode diagram
(1) When the magnitude-frequency curve crosses the 0dB line, if the corresponding phase angle is larger than -1800, then it’s stable. Vice versa. The crossing frequency with the 0dB line is called magnitude crossing frequency, denoted as ωc. (2) When the phase-frequency curve crosses the -1800 line, if the corresponding magnitude is negative, then it’s stable. Vice versa. The crossing frequency with the 0dB line is called phase crossing frequency, denoted as ωg.
20 dB

1

ω =7 16 c 5 10

1d 5B

50 100

ω

?

π
2

? π
3 π ? 2

γ =55

ω
ω g

The margin of magnitude : The margin of phase :
20 dB

1 Kg = G (jω ) H (jω )

ω =ωg

γ c = 180o + ? (ω c )
ω

1

ωc = 7 16 10 5

15dB

50

100

?

π
2


? 3π 2

γ = 55

ω
ωg

To obtain a favorable performance, the magnitude margin should be larger than 6dB, while the phase margin should go between 30-60°. °

Example 4:For a system: :

-

K s ( s + 1)( s + 5 )

Calculate the magnitude margin and phase margin when K=10 and K=100. K=100
K=10 -12dB 0dB +8dB

+21o -180
o

-30o

6-1 Introduction
What’s compensation or correction of a control system ? K The OL of the system: G(s)H(s) = s(Ts +1)(s +1) How to make it stable. According to the Routh criterion, we can get:
T +1 1 K< =1+ (K > 0 T > 0) T T

But for the system:

K G(s)H(s) = 2 s (Ts +1)

According to Routh criterion, this system cannot be stable only varying K or T.

K(τ s +1) If we make: G(s)H(s) = 2 s (Ts +1)
This closed-loop system can be stable.

τ >T

We make the system stable by adding a component. This procedure is called the compensation or correction. Definition of compensation: Adding a component, which makes the system’s performance to be improved, other than only by varying the system’s parameters, this procedure is called the compensation or correction of the system.

Compensator: The compensator is an additional component that is inserted into a control system to compensate for a deficient performance.
K Example: G(s)H(s) = 2 , to add an τs+1 component, s (Ts+1) the systemcan be stable, τs+1 is a compensator.

Types of the compensation
The transfer function of the compensator is designated as Gc (s), and according to the location of Gc (s) in the structure of the system, we can get several types:

(1) Cascade compensation (2) Feedback compensation (3) Both cascade and feedback compensation (4) Feed-forward compensation

Cascade compensation

Features : simple but the effects to be restricted.

Feedback compensation
R(s)

-

-

G0 ( s ) GC

C(s)

R(s)

C(s)

-

G 10

-

G 20
GC

Features: complicated but noise limiting, the effects are better than the cascade compensation.

Both cascade and feedback compensation
R(s) C(s)

-

GC1

-

G0

GC 2

Features: have advantages both of cascade and feedback compensation.

Feed-forward compensation
GC
R(s) F(s)

GC

+

C(s) R(s)

-

G10

G20

-

G10

+

C(s)
G20

For input For disturbance(voice) Features: theoretically we can make the error of a system to be zero and no effects to the transient performance of the system.

6-2 Operation analysis of the basic compensators
PID controller
Transfer function:
1 Gc(s) = Kp (1+ + τDs) τI s Kp 1 = Kp + KI + KDs → KI = ; KD = Kpτ D s τI

P-- proportional controller →promoting sensitivity I -- integrating controller →clearing ess D-- differential controller →improving stability

PD controller

transfer function: Gc (s) = Kp + KDs
G (s) C

Assuming: G(s) =

R(s)+

ω

s(s + 2ξωn )

2 n



Kp
KDs

+ +

G(s)

C(s)

The open ? loop transfer function of the compensated

ωn2 (KP + KDs) system is: Gc (s)G(s) = s(s + 2ξωn )
It shows that the PD controller is equivalent to adding a KP open ? loop zero at : s = ? KD

Effects of PD controller: 1) PD controller does not alter the system type; 2) PD controller improve the system’s stability (to increase damping and reduce maximum overshoot); 3) PD controller reduce the rise time and settling time; 4) PD controller increase BW(Band Width) and improve GM(Kg), PM(γc) .

- bring in the noise !

1 PI controller Transfer function : Gc (s) = K p + KI s R(s) + + C(s) Kp G(s) ωn2 - + Assum : G(s) = ing 1 KI s(s + 2ξωn ) GC (s) s
The op ? loop transfer function of the com ensate d systemis : en p 1

ωn2(KP + KI ) ω 2(K s + K ) s = n P I Gc (s)G(s) = s(s + 2ξωn ) s2(s + 2ξωn )
It show that the PI controller is eq alent to ad ing a op ? loop s uiv d en KI zero at : s = ? and a p at : s = 0 ole KP

Effects of PI controller: 1) Increase the system’s type-clear the steady-state error ; - 2) reduce BW(Band Width) and GM(Kg), PM(γc); beneficial to the noise limiting , not beneficial to the system’s stability.

PID controller
R(s)

Transfer function: Gc(s) = K p + KI 1 + KDs s

-

Kp
KI 1 s

+

G(s)

C(s)

KDs

G C (s )

PID controller have advantages both of PI and PD.

Circuits of PID
R2 ur R1 C ur R1 R2

_
u0

_
u0

+ PI controller
R2 ur R1 C2

C

+ PD controller

_
u0

C1

+ PID controller


更多相关文档:

现代控制工程CH06 Compensation of the Control Systems.ppt

现代控制工程CH06 Compensation of the Control Systems 现代控制工程CH06 Compensation of the Control Systems现代控制工程CH06 Compensation of the Control Systems隐...

Chapter6 The Compensation of the Linear Control Sys....ppt

Chap 6 The Compensation of the linear control systems P553 1 Chap 6 The...现代控制工程CH06 Compe... 暂无评价 17页 1下载券 ON THE ISS PROPERTY...

...of compensation degrees in power control systems_图文.pdf

The determination and realization of compensation degrees in power control systems_电力/水利_工程科技_专业资料。The determination and realization of compensation...

现代控制工程CH03-2 1-order and 2-order system_图文.ppt

现代控制工程CH03-2 1-order and 2-order system_经济学_高等教育_教育专区...while the overdamped systems is blunt in response, and act slowly, so, ...

Introduction to control systems_图文.pdf

Introduction to Feedback Control Theory FIGURE 1.1 The objective is to ...Lead and/or compensation Mathematical Models of Systems Definition of Mathematical...

A_New_Compensation_Technique_for_Backlash_in_Positi....pdf

for_Backlash_in_Position_Control_Systems_with_Elasticity_电子/电路_工程科技_...Backlash compensation, nonlinear systems, position control The presence of backlas...

Topic I 1 Introduction to Control Systems_图文.pdf

Topic I 1 Introduction to Control Systems_理学_高等教育_教育专区。自动控制(...(Heating system) Compensation for disturbances (steering & all of the above...

Understanding Dancer Tension Control Systems_图文.pdf

Understanding Dancer Tension Control Systems_材料科学_工程科技_专业资料。浮动辊...Control Gain + Unwind Gain) w/o Gain CompensationThe Past” Gain Full...

Process Control Systems.ppt

Process Control Systems_电子/电路_工程科技_专业...the practice of process control and its ...Ratio Control. Time-delay compensation. ...

Radiometric Compensation of Global Illumination Eff....pdf

Compensation of Global Illumination Effects with Projector-Camera Systems_专业...Conclusion The light transport matrix of a projector-camera con?guration ...

...CompensationforPeakCurrentModeControl_图文.pdf

SlopeCompensationforPeakCurrentModeControl_物理_自然...grote@lea.upb.de 2 DELTA Energy Systems GmbH, ...In order to eliminate the drawbacks of peak ...

...for the Compensation of the SAR Range_图文.pdf

A New Method for the Compensation of the SAR Range_信息与通信_工程科技_...and the coordinate systems (2, r ) and (z’, r’) have been fixed ...

Compensation of Phase Noise in OFDM Wireless System....pdf

Compensation of Phase Noise in OFDM Wireless ...eld to make the real systems more reliable and ...the closed-loop control mechanism tracks the phase...

Compensation of Thermo-elastic Machine Tool Deforma....pdf

Control internal Data_电子/电路_工程科技_专业资料...The compensation of the load influence of the ...For the mathematical modelling linear systems of ...

Input_Delay_Compensation_for_Forward_Complete_and_S....pdf

Compensation_for_Forward_Complete_and_Strict-Feedforward_Nonlinear_Systems-GEp_...The size of the control input is due to the need to compensate for a ...

DS_CONTROL_SYSTEMS.pdf

Control Systems Industrial Produkt Product System ...the injection-pump lever of diesel engines to be...with a PTFE membrane for pressure compensation. Three...

...for A Class of nonlinear MIMO systems_图文.pdf

Control for A Class of nonlinear MIMO systems_信息与通信_工程科技_专业资料...control and sliding mode Being the auxiliary compensation, control are ...

Analysis on the control principle of the active DC ....pdf

Analysis on the control principle of the active DC filter in the Lindome ...systems, including harmonic filtering, reactive power compensation, power factor...

Non-linea r auto-disturbance rejection control_图文.pdf

of the state feedback errors and the compensation of the total disturbances...[19] HAN J.Q.: ‘Nonlinear design method for control systems design’. ...

...The Differences in Political, Economic, and Legal Systems....ppt

CH03 Management Around The World and The Differences in Political, Economic, and Legal Systems Review Questions 1. What is the development of international...

更多相关标签:
网站地图

文档资料共享网 nexoncn.com copyright ©right 2010-2020。
文档资料共享网内容来自网络,如有侵犯请联系客服。email:zhit325@126.com